Work Description

Date: 22 June, 2023

Dataset Title: Persistent Homology as a Heterogeneity Metric for Predicting Pore Size Change in Dissolving Carbonates

Dataset Creators: E.P. Thompson, B.R. Ellis

Dataset Contact: Brian Ellis (brellis@umich.edu)

Funding: National Science Foundation (NSF) CAREER Grant No. 1943726; Alfred P. Sloan Foundation (APSF) 202-12,466

Key Points:
- Persistent homology applied to 3D imagery provides detailed information about the size, connectivity, and heterogeneity of pore features
- Permeability increase in dissolving carbonates due to growth of large, connected pore bodies with little intrusion into disconnected pores
- Sample with highly heterogeneous pore size saw an increase in along-core pore size homogeneity after reaction

Research Overview:
Accurate prediction of physical alterations in carbonate reservoirs under dissolution is critical for development of subsurface energy technologies. The impact of mineral dissolution on flow characteristics depends on the connectivity
and tortuosity of the pore network. Persistent homology is a tool from algebraic topology that describes the size and connectivity of topological features. When applied to 3D X-ray computed tomography (XCT) imagery of rock cores, it
provides a novel metric of pore network heterogeneity. Prior works have demonstrated the efficacy of persistent homology in predicting flow properties in numerical simulations of flow through porous media. Its ability to combine size,
spatial distribution, and connectivity information make it a promising tool for understanding reactive transport in complex pore networks, yet limited work has been done to apply persistence analysis to experimental studies on natural
rocks. In this study, three limestone cores were imaged by XCT before and after acid-driven dissolution flow-through experiments. Each XCT scan was analyzed using persistent homology. In all three rocks, permeability increase was
driven by the growth of large, connected pore bodies. The two most homogenous samples saw an increased effect nearer to the flow inlet, suggesting emerging preferential flow paths as the reaction front progresses. The most
heterogeneous sample showed an increase in along-core homogeneity during reaction. Variability of persistence showed moderate positive correlation with pore body size increase. Persistence heterogeneity analysis could be used to
anticipate where greatest pore size evolution may occur in a reservoir targeted for subsurface development, improving confidence in project viability.

Methodology:
The data are XCT imagery processed using ImageJ (version 2.9.0) and analyzed using the diamorse package for Python (https://github.com/AppliedMathematicsANU/diamorse)

Instrument and/or Software specifications
- XCT images taken using Nikon XT H 225 ST Industrial CT scanner

Files contained here:
In all of the following folders, data are available for the three samples (Indiana (IL04), Edwards (EY03), and Lueders (LU03) Limestones) at the three stages of reaction (Pre, Post1, and Post2) and are labeled accordingly. Where data were subdivided for
along-core analysis, the order of subsections is as follows (from inlet to outlet):
Indiana_Pre and Edwards_Pre: 01 02 03 04 05 06 07 08 09 10
All other datasets: 10 09 08 07 06 05 04 03 02 01
For analysis Indiana uses sections 2-9, Edwards and Lueders uses sections 1-8

- original_tomograms folder:
These are the original tomograms taken from the XCT scanner. Files are 3D .tif stacks. .tif stacks are named __rawstack.tif (ex. original_tomograms/Edwards03_Pre_rawstack.tif)

- segmented_tomograms folder:
These tomograms have been processed to reduce noise, enhance contrast, and reduce beam hardening. Binary segmentation was performed using Trainable Weka Segmentation (For additional detail please see the Related Publication cited below).
Files are 3D .tif stacks. Samples are named __seg_full.tif (ex. segmented_tomograms/ey03_pre_seg_full.tif)

- sedt_files folder:
These are the Signed Euclidean Distance Transform files generated using diamorse. Files are in folders of .nc files sorted by subsection. The diamorse package generates a folder for each subsection, containing .nc files labeled block0000000#.nc. Persistence analyis is performed on the folder that contains the block files (for more detail on use of these files, please see the diamorse readme file in the software folder). For example, sedt_files/tomo_floatey03_pre_01_IMP_SEDT_nc references the Edwards03, pre-reaction, subsection 01 SEDT files. This folder contains blocks 00000000 through 00000003.

- persistence_pairs folders:
These are the output of the diamorse persistence analysis. Files are .txt files. Files are sorted by sample and named /___pairs.txt (ex. persistence_pairs/ey03_pairs/ey03_pre_01_pairs.txt)
Each file is a tab-delimited table of persistence data with a header labeling the columns: # format:
Birth and death values refer to the birth and death distances of each pore feature, dimension refers to the feature's topological dimension. Creator and destructor xyz provide coordinates within the image data where creation and destruction occurred. Weight is a feature of the diamorse analysis that was not used for this study.

- software folder:
This contains a copy of the diamorse python package, downloaded from https://github.com/AppliedMathematicsANU/diamorse on June 15, 2023. Please see following license statement regarding use and distribution of this software package:

The MIT License (MIT)
Copyright (c) 2015 The Australian National University
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Related publication(s)
Thompson, E.P.; Ellis, B.R. (2023) Persistent Homology as a Heterogeneity Metric for Predicting Pore Size Change in Dissolving Carbonates. Forthcoming.

Use and Access:
This data set is publicly available through the Deep Blue Repository at the University of Michigan.

To Cite Data:
Thompson, E.P., Ellis, B.R. Persistent Homology as a Heterogeneity Metric for Predicting Pore Size Change in Dissolving Carbonates [Data set]. University of Michigan - Deep Blue. https://doi.org/10.7302/x0zz-m727